On the energy of some special classes of graphs

Date of Publication

2010

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Francis Joseph H. Campena

Defense Panel Chair

Isagani B. Jos

Defense Panel Member

Michele G. Tan
Christopher Thomas R. Cruz

Abstract/Summary

This study is an exposition of the article called Energy of a Graph is never the square root of an Odd Integer by S. Pirzada and I. Gutman. The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this thesis, the theorem initially proved by Bapat and Pati (Bull. Kerala Math. Assoc., 1 (2004), 129-134) is included: (a) E(G) is never an odd integer. The main objective of this study is to show that (b) E(G) is never the square root of an odd integer. In addition, if r and s are integers such that r ≥ 1 and 0 ≤ s ≤ -1 and q is an odd integer, then E(G) cannot be of the form (2sq)1/r, a result that implies (a) and (b) as special cases.

Abstract Format

html

Language

English

Accession Number

TU16008

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

xi, 51 leaves, illustrations, 28 cm.

Keywords

Graph theory

Embargo Period

4-15-2021

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